Question

A store received a shipment of 400 skateboard wheels. After four days, 328 of the skateboard wheels are left. After eight days, 256 skateboard wheels are left.

A. Write an equation that represents the number Y
B. Use a linear equation to predict how many skateboard wheels will be left after 10 days.
C. After how many days should the store plan to receive a new shipment of skateboard wheels so they don’t run out?
D. What does the slope of the equation represent? What does the Y-intercept represent?

Answer 1

To represent the number of skateboard wheels left, the equation Y = -18x + 400 can be used, where Y is the number of wheels and x is the number of days. To predict the wheels left after 10 days, plug x = 10 into the equation. The store should plan to receive a new shipment of skateboard wheels when Y = 0, so solve the equation Y = -18x + 400 for x.

Step-by-step explanation:

To write an equation that represents the number of skateboard wheels left after a certain number of days, we can use the equation:

Y = mx + b

where Y is the number of skateboard wheels left, x is the number of days, m is the slope, and b is the y-intercept.

In this case, we're given that after four days, there are 328 skateboard wheels left. This gives us the point (4, 328). We're also given that after eight days, there are 256 skateboard wheels left. This gives us the point (8, 256).

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the two given points, we get:

m = (256 - 328) / (8 - 4) = -18

Now we can use the slope-intercept form of a linear equation:

Y = mx + b

Plugging in the slope and one of the given points, we get:

256 = -18(8) + b

b = 400

So the equation that represents the number of skateboard wheels left is:

Y = -18x + 400

To predict how many skateboard wheels will be left after 10 days, we can plug in x = 10 into the equation:

Y = -18(10) + 400 = 220